Thank you all for the replies. Called Flying Blue three times (twice in the US and once in the Netherlands). Was told three times that if their system shows no availability, there is no availability. No exceptions. Mentioned the long sells, same response.
Was ready to give up, but sent Flying Blue an email. Received a call from Flying Blue within five minutes (wow!). Was informed that in order to see Korean availability, the Flying Blue employees need to search in a special and apparently quite secret way (not sure what way). And indeed there was lots of availability....